We report the large effort that is producing comprehensive high-level young star cluster (YSC) catalogs for a significant fraction of galaxies observed with the Legacy ExtraGalactic UV Survey (LEGUS) Hubble treasury program. We present the methodology developed to extract cluster positions, verify their genuine nature, produce multiband photometry (from NUV to NIR), and derive their physical properties via spectral energy distribution fitting analyses. We use the nearby spiral galaxy NGC 628 as a test case for demonstrating the impact that LEGUS will have on our understanding of the formation and evolution of YSCs and compact stellar associations within their host galaxy. Our analysis of the cluster luminosity function from the UV to the NIR finds a steepening at the bright end and at all wavelengths suggesting a dearth of luminous clusters. The cluster mass function of NGC 628 is consistent with a power-law distribution of slopes $\sim -2$ and a truncation of a few times 105 $M\odot$. After their formation, YSCs and compact associations follow different evolutionary paths. YSCs survive for a longer time frame, confirming their being potentially bound systems. Associations disappear on timescales comparable to hierarchically organized star-forming regions, suggesting that they are expanding systems. We find mass-independent cluster disruption in the inner region of NGC 628, while in the outer part of the galaxy there is little or no disruption. We observe faster disruption rates for low mass (≤104 $M\odot$) clusters, suggesting that a mass-dependent component is necessary to fully describe the YSC disruption process in NGC 628.